| Résume | A result obtained by A. Macintyre and J. Derakhshan states that the theory of a Henselian valued field of mixed characteristic, finite ramification, perfect residue field and whose value group is a Z-group, is model complete in the language of rings if the theory of the residue field is model complete in the language of rings. In this talk we will see how this result can be generalized to henselian valued fields with the same properties but with different value groups. We will address the case of value groups with finite spines and value groups elementarily equivalent to the lexicografical product of Z with minimal positive element. We will see in which languages these groups are model complete and we will define a one sorted language in which the theory of the respective valued field is model complete, assuming that the residue field is model complete in the language of rings. It follows that the theories of some infinite non-algebraic extensions of the field of p-adic numbers are model complete in the respective language. |
